Torsion group Z/5Z, rank = 9


Klagsbrun (2020)

y2 + xy = x3 - 1271376476514788123979112128312980x 
         + 248131717764014678423337299444388036083025142487952

	Torsion points: 

O, [81072141178321384, -26036910848358757113626132], 
[81072141178321384, 26036910767286615935304748], 
[-36657363539197856, 15667745365287028047043828], 
[-36657363539197856, -15667745328629664507845972]

	Independent points of infinite order: 

P1 = [-14321012301695918, -16229664177818781437394920]
P2 = [10577225558843944, 15357976348226927412589228]
P3 = [-27958139052681656, -16180956320789973349299572]
P4 = [-12613875480867206, -16191408531364576440288722]
P5 = [-65967350243410856, -6703097091935764599385172]
P6 = [-15013641556597656, -16243013630316451507874772]
P7 = [31847899142275944, 15490126243819265114358828]
P8 = [21591375902627529544, 100327476981383170234740234028]
P9 = [160382787921354544, 64573162419225467324709028]

Some curves with torsion group Z/5Z and rank = 6, 7 or 8
High rank curves with prescribed torsion Andrej Dujella home page